23 people attend a party. Each person shakes hands with at least two other people. What is the minimum possible number of handshakes?
Answer: If each person shakes hands with exactly two other people, then there will be $\frac{23 \cdot 2}{2} = \boxed{23}$ handshakes. To achieve 23 handshakes, we arrange the participants in a circle. Each person shakes hands with the two people next to him or her.